The graph shows two lines representing the equations y = 2x + 5 and x + y = 1
Which ordered pair is in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1?
(-5,0)
(0,7)
(5,0)
(0,-7)
To determine which ordered pair is in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1, we need to plug in the x and y values of each ordered pair into both inequalities and see which ones satisfy both conditions.
1. (−5,0):
y ≥ 2x + 5
0 ≥ 2(-5) + 5
0 ≥ -10 + 5
0 ≥ -5 (True)
x + y ≤ 1
-5 + 0 ≤ 1
-5 ≤ 1 (True)
Since both inequalities are true for (−5,0), this ordered pair is in the solution set.
2. (0,7):
y ≥ 2x + 5
7 ≥ 2(0) + 5
7 ≥ 0 + 5
7 ≥ 5 (True)
x + y ≤ 1
0 + 7 ≤ 1
7 ≤ 1 (False)
Since the second inequality is not true for (0,7), this ordered pair is not in the solution set.
3. (5,0):
y ≥ 2x + 5
0 ≥ 2(5) + 5
0 ≥ 10 + 5
0 ≥ 15 (False)
x + y ≤ 1
5 + 0 ≤ 1
5 ≤ 1 (False)
As both inequalities are not true for (5,0), this ordered pair is not in the solution set.
4. (0,−7):
y ≥ 2x + 5
-7 ≥ 2(0) + 5
-7 ≥ 0 + 5
-7 ≥ 5 (False)
x + y ≤ 1
0 + (-7) ≤ 1
-7 ≤ 1 (True)
Since second inequality is true for (0,−7), this ordered pair is in the solution set.
Therefore, the ordered pair in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1 is (-5,0) and (0,-7).